A charged particle of mass `m` and charge `q` is released from rest in an electric field of constant magnitude `E`. The kinetic energy of the particle after time `t` is

Options

A. `(E^(2) q^(2)t^(2))/(2m)`
B. `(2E^(2) t^(2))/(mq)`
C. `(Eqm)/(2t)`
D. `(Eq^(2)m)/(2t^(2))`

Answer

A

Explanation

Here, u = 0
The acceleration of the particle is `a = (F)/(m) = (qE)/(m)`
Using, `v = u + at = 0 + (qE)/(m)t`
The kinetic energy of the particle after time t is
`K = (1)/(2) mv^(2) = (mq^(2)E^(2) t^(2))/(2m^(2)) = (E^(2)q^(2)t^(2))/(2m)` (Using (i))